Science

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Light – Reflection and

Refraction

CHAPTER

e see a variety of objects in the world ar

ound us. However, we are

unable to see anything in a dark room. On lighting up the room,

things become visible. What makes things visible? During the day, the

sunlight helps us to see objects. An object reflects light that falls on it.

This reflected light, when received by our eyes, enables us to see things.

We are able to see through a transparent medium as light is transmitted

through it. There are a number of common wonderful phenomena

associated with light such as image formation by mirrors, the twinkling

of stars, the beautiful colours of a rainbow, bending of light by a medium

and so on. A study of the properties of light helps us to explore them.

By observing the common optical phenomena around us, we may

conclude that light seems to travel in straight lines. The fact that a small

source of light casts a

sharp shadow of an opaque object points to this

straight-line path of light, usually indicated as a ray of light.

More to Know!

If an opaque object on the path of light becomes very small, light has a tendency to

bend around it and not walk in a straight line – an effect known as the diffraction of

light. Then the straight-line treatment of optics using rays fails. To explain phenomena

such as diffraction, light is thought of as a wave, the details of which you will study

in higher classes. Again, at the beginning of the 20

century, it became known that

the wave theory of light often becomes inadequate for treatment of the interaction of

light with matter, and light often behaves somewhat like a stream of particles. This

confusion about the true nature of light continued for some years till a modern

quantum theory of light emerged in which light is neither a ‘wave’ nor a ‘particle’ –

the new theory reconciles the particle properties of light with the wave nature.

In this Chapter, we shall study the phenomena of reflection and

refraction of light using the straight-line propagation of light. These basic

concepts will help us in the study of some of the optical phenomena in

nature. We shall try to understand in this Chapter the reflection of light

by spherical mirrors and refraction of light and their application in real

life situations.

9.1 REFLECTION OF LIGHT9.1 REFLECTION OF LIGHT

9.1 REFLECTION OF LIGHT

A highly polished surface, such as a mirror, reflects most of the light

falling on it. You are already familiar with the laws of reflection of light.

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Let us recall these laws –

(i) The angle of incidence is equal to the angle of reflection, and

(ii) The incident ray, the normal to the mirror at the point of incidence

and the reflected ray, all lie in the same plane.

These laws of reflection are applicable to all types of reflecting surfaces

including spherical surfaces. You are familiar with the formation of image

by a plane mirror. What are the properties of the image? Image formed

by a plane mirror is always virtual and erect. The size of the image is

equal to that of the object. The image formed is as far behind the mirror

as the object is in front of it. Further, the image is laterally inverted.

How would the images be when the reflecting surfaces are curved? Let

us explore.

Activity 9.1Activity 9.1

Activity 9.1

n Take a large shining spoon. Try to view your face in its curved

surface.

n Do you get the image? Is it smaller or larger?

n Move the spoon slowly away from your face. Observe the image.

How does it change?

n Reverse the spoon and repeat the Activity. How does the image

look like now?

n Compare the characteristics of the image on the two surfaces.

The curved surface of a shining spoon could be considered as a curved

mirror. The most commonly used type of curved mirror is the spherical

mirror. The reflecting surface of such mirrors can be considered to form

a part of the surface of a sphere. Such mirrors, whose reflecting surfaces

are spherical, are called spherical mirrors. We shall now study about

spherical mirrors in some detail.

9.2 SPHERIC9.2 SPHERIC

9.2 SPHERIC

AL MIRRORSAL MIRRORS

AL MIRRORS

The reflecting surface of a spherical mirror may be curved inwards or

outwards. A spherical mirror, whose reflecting surface is curved inwards,

that is, faces towards the centre of the sphere, is called a concave mirror.

A spherical mirror whose reflecting surface is curved outwards, is called

a convex mirror. The schematic representation of these mirrors is shown

in Fig. 9.1. You may note in these diagrams that the back

of the mirror is shaded.

You may now understand that the surface of the spoon

curved inwards can be approximated to a concave mirror

and the surface of the spoon bulged outwards can be

approximated to a convex mirror.

Before we move further on spherical mirrors, we need to

recognise and understand the meaning of a few terms. These

terms are commonly used in discussions about spherical

mirrors. The centre of the reflecting surface of a spherical

mirror is a point called the pole. It lies on the surface of the

mirror. The pole is usually represented by the letter P.

Figure 9.1Figure 9.1

Figure 9.1

Schematic representation of spherical

mirrors; the shaded side is non-reflecting.

(a) Concave mirror (b) Convex mirror

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The reflecting surface of a spherical mirror forms a part of a sphere.

This sphere has a centre. This point is called the centre of curvature of

the spherical mirror. It is represented by the letter C. Please note that the

centre of curvature is not a part of the mirror. It lies outside its reflecting

surface. The centre of curvature of a concave mirror lies in front of it.

However, it lies behind the mirror in case of a convex mirror. You may

note this in Fig.9.2 (a) and (b). The radius of the sphere of which the

reflecting surface of a spherical mirror forms a part, is called the radius

of curvature of the mirror. It is represented by the letter R. You may note

that the distance PC is equal to the radius of curvature. Imagine a straight

line passing through the pole and the centre of curvature of a spherical

mirror. This line is called the principal axis. Remember that principal

axis is normal to the mirror at its pole. Let us understand an important

term related to mirrors, through an Activity.

Activity 9.2Activity 9.2

Activity 9.2

CAUTION: Do not look at the Sun directly or even into a mirror

reflecting sunlight. It may damage your eyes.

n Hold a concave mirror in your hand and direct its reflecting surface

towards the Sun.

n Direct the light reflected by the mirror on to a sheet of paper held

close to the mirror.

n Move the sheet of paper back and forth gradually until you find

on the paper sheet a bright, sharp spot of light.

n Hold the mirror and the paper in the same position for a few

minutes. What do you observe? Why?

The paper at first begins to burn producing smoke. Eventually it

may even catch fire. Why does it burn? The light from the Sun is converged

at a point, as a sharp, bright spot by the mirror. In fact, this spot of light

is the image of the Sun on the sheet of paper. This point is

the focus of the concave mirror. The heat produced due to

the concentration of sunlight ignites the paper. The distance

of this image from the position of the mirror gives the

approximate value of focal length of the mirror.

Let us try to understand this observation with the help

of a ray diagram.

Observe Fig.9.2 (a) closely. A number of rays parallel

to the principal axis are falling on a concave mirror. Observe

the reflected rays. They are all meeting/intersecting at a

point on the principal axis of the mirror. This point is called

the principal focus of the concave mirror. Similarly, observe

Fig. 9.2 (b). How are the rays parallel to the principal axis,

reflected by a convex mirror? The reflected rays appear to

come from a point on the principal axis. This point is called

the principal focus of the convex mirror. The principal focus

is represented by the letter F. The distance between the

pole and the principal focus of a spherical mirror is called

the focal length. It is represented by the letter f.

Figure 9.2Figure 9.2

Figure 9.2

(a) Concave mirror

(b)

Convex mirror

(b)

(a)

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The reflecting surface of a spherical mirror is by-and-large spherical.

The surface, then, has a circular outline. The diameter of the reflecting

surface of spherical mirror is called its aperture. In Fig.9.2, distance MN

represents the aperture. We shall consider in our discussion only such

spherical mirrors whose aperture is much smaller than its radius of

curvature.

Is there a relationship between the radius of curvature R, and focal

length f, of a spherical mirror? For spherical mirrors of small apertures,

the radius of curvature is found to be equal to twice the focal length. We

put this as R = 2f . This implies that the principal focus of a spherical

mirror lies midway between the pole and centre of curvature.

9.2.1 Image Formation by Spherical Mirrors

You have studied about the image formation by plane mirrors. You also

know the nature, position and relative size of the images formed by them.

How about the images formed by spherical mirrors? How can we locate

the image formed by a concave mirror for different positions of the object?

Are the images real or virtual? Are they enlarged, diminished or have

the same size? We shall explore this with an Activity.

Activity 9.3Activity 9.3

Activity 9.3

You have already learnt a way of determining the focal length of a

concave mirror. In Activity 9.2, you have seen that the sharp bright

spot of light you got on the paper is, in fact, the image of the Sun. It

was a tiny, real, inverted image. You got the approximate focal length

of the concave mirror by measuring the distance of the image from

the mirror.

n Take a concave mirror. Find out its approximate focal length in

the way described above. Note down the value of focal length. (You

can also find it out by obtaining image of a distant object on a

sheet of paper.)

n Mark a line on a Table with a chalk. Place the concave mirror on

a stand. Place the stand over the line such that its pole lies over

the line.

n Draw with a chalk two more lines parallel to the previous line

such that the distance between any two successive lines is equal

to the focal length of the mirror. These lines will now correspond

to the positions of the points P, F and C, respectively. Remember –

For a spherical mirror of small aperture, the principal focus F lies

mid-way between the pole P and the centre of curvature C.

n Keep a bright object, say a burning candle, at a position far beyond

C. Place a paper screen and move it in front of the mirror till you

obtain a sharp bright image of the candle flame on it.

n Observe the image carefully. Note down its nature, position and

relative size with respect to the object size.

n Repeat the activity by placing the candle – (a) just beyond C,

(b) at C, (c) between F and C, (d) at F, and (e) between P and F.

n In one of the cases, you may not get the image on the screen.

Identify the position of the object in such a case. Then, look for its

virtual image in the mirror itself.

n Note down and tabulate your observations.

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You will see in the above Activity that the nature, position and size of

the image formed by a concave mirror depends on the position of the

object in relation to points P, F and C. The image formed is real for some

positions of the object. It is found to be a virtual image for a certain other

position. The image is either magnified, reduced or has the same size,

depending on the position of the object. A summary of these observations

is given for your reference in Table 9.1.

Table 9.1 Image formation by a concave mirror for different positions of the object

Position of the Position of the Size of the Nature of the

object image image image

At infinity At the focus F Highly diminished, Real and inverted

point-sized

Beyond C Between F and C Diminished Real and inverted

At C At C Same size Real and inverted

Between C and F Beyond C Enlarged Real and inverted

At F At infinity Highly enlarged Real and inverted

Between P and F Behind the mirror Enlarged Virtual and erect

9.2.2 Representation of Images Formed by Spherical

Mirrors Using Ray Diagrams

We can also study the formation of images by spherical mirrors by

drawing ray diagrams. Consider an extended object, of finite size, placed

in front of a spherical mirror. Each small portion of the extended object

acts like a point source. An infinite number of rays originate from each

of these points. To construct the ray diagrams, in order to locate the

image of an object, an arbitrarily large number of rays emanating from a

point could be considered. However, it is more convenient to consider

only two rays, for the sake of clarity of the ray diagram. These rays are

so chosen that it is easy to know their directions after reflection from the

mirror.

The intersection of at least two reflected rays give the position of image

of the point object. Any two of the following rays can be considered for

locating the image.

(i) A ray parallel to the principal

axis, after reflection, will pass

through the principal focus

in case of a concave mirror

or appear to diverge from

the principal focus in

case of a convex mirror.

This is illustrated in Fig.9.3

(a) and (b).

(a) (b)

FigureFigure

Figure

9.39.3

9.3

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(ii) A ray passing through the

principal focus of a concave

mirror or a ray which is

directed towards the

principal focus of a convex

mirror, after reflection, will

emerge parallel to the

principal axis. This is

illustrated in Fig.9.4 (a)

and (b).

(iii) A ray passing through the

centre of curvature of a

concave mirror or directed

in the direction of the centre

of curvature of a convex

mirror, after reflection, is

reflected back along the

same path. This is

illustrated in Fig.9.5 (a) and

(b). The light rays come back

along the same path

because the incident rays

fall on the mirror along the

normal to the reflecting

surface.

(iv) A ray incident obliquely to

the principal axis, towards

a point P (pole of the mirror),

on the concave mirror

[Fig. 9.6 (a)] or a convex

mirror [Fig. 9.6 (b)], is

reflected obliquely. The

incident and reflected rays

follow the laws of reflection

at the point of incidence

(point P), making equal

angles with the principal axis.

(a) (b)

Figure 9.4Figure 9.4

Figure 9.4

Remember that in all the above cases the laws of reflection are followed.

At the point of incidence, the incident ray is reflected in such a way that

the angle of reflection equals the angle of incidence.

(a) Image formation by Concave Mirror

Figure 9.7 illustrates the ray diagrams for the formation of image

by a concave mirror for various positions of the object.

(b)

(a)

Figure 9.5Figure 9.5

Figure 9.5

(a) (b)

Figure 9.6Figure 9.6

Figure 9.6

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Figure 9.7Figure 9.7

Figure 9.7 Ray diagrams for the image formation by a concave mirror

Activity 9.4Activity 9.4

Activity 9.4

n Draw neat ray diagrams for each position of the object shown in

Table 9.1.

n You may take any two of the rays mentioned in the previous section

for locating the image.

n Compare your diagram with those given in Fig. 9.7.

n Describe the nature, position and relative size of the image formed

in each case.

n Tabulate the results in a convenient format.

Uses of concave mirrors

Concave mirrors are commonly used in torches, search-lights and

vehicles headlights to get powerful parallel beams of light. They are

often used as shaving mirrors to see a larger image of the face. The

dentists use concave mirrors to see large images of the teeth of patients.

Large concave mirrors are used to concentrate sunlight to produce

heat in solar furnaces.

(b) Image formation by a Convex Mirror

We studied the image formation by a concave mirror. Now we shall

study the formation of image by a convex mirror.

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We consider two positions of the object for studying the image formed

by a convex mirror. First is when the object is at infinity and the second

position is when the object is at a finite distance from the mirror. The ray

diagrams for the formation of image by a convex mirror for these two

positions of the object are shown in Fig.9.8 (a) and (b), respectively. The

results are summarised in Table 9.2.

Activity 9.5Activity 9.5

Activity 9.5

n Take a convex mirror. Hold it in one hand.

n Hold a pencil in the upright position in the other hand.

n Observe the image of the pencil in the mirror. Is the image erect or

inverted? Is it diminished or enlarged?

n Move the pencil away from the mirror slowly. Does the image

become smaller or larger?

n Repeat this Activity carefully. State whether the image will move

closer to or farther away from the focus as the object is moved

away from the mirror?

Figure 9.8 Figure 9.8

Figure 9.8 Formation of image by a convex mirror

You have so far studied the image formation by a plane mirror, a

concave mirror and a convex mirror. Which of these mirrors will give the

full image of a large object? Let us explore through an Activity.

Activity 9.6Activity 9.6

Activity 9.6

n Observe the image of a distant object, say a distant tree, in a

plane mirror.

n Could you see a full-length image?

Table 9.2 Nature, position and relative size of the image formed by a convex mirror

Position of the Position of the Size of the Nature of the

object image image image

At infinity At the focus F, Highly diminished, Virtual and erect

behind the mirror point-sized

Between infinity Between P and F, Diminished Virtual and erect

and the pole P of behind the mirror

the mirror

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n Try with plane mirrors of different sizes. Did you see the entire

object in the image?

n Repeat this Activity with a concave mirror. Did the mirror show

full length image of the object?

n Now try using a convex mirror. Did you succeed? Explain your

observations with reason.

You can see a full-length image of a tall building/tree in a small

convex mirror. One such mirror is fitted in a wall of Agra Fort facing Taj

Mahal. If you visit the Agra Fort, try to observe the full image of Taj

Mahal. To view distinctly, you should stand suitably at the terrace

adjoining the wall.

Uses of convex mirrors

Convex mirrors are commonly used as rear-view (wing) mirrors in

vehicles. These mirrors are fitted on the sides of the vehicle, enabling the

driver to see traffic behind him/her to facilitate safe driving. Convex

mirrors are preferred because they always give an erect, though

diminished, image. Also, they have a wider field of view as they are curved

outwards. Thus, convex mirrors enable the driver to view much larger

area than would be possible with a plane mirror.

QUESTIONS

1. Define the principal focus of a concave mirror.

2. The radius of curvature of a spherical mirror is 20 cm. What is its focal

length?

3. Name a mirror that can give an erect and enlarged image of an object.

4. Why do we prefer a convex mirror as a rear-view mirror in vehicles?

9.2.3 Sign Convention for Reflection by Spherical Mirrors

While dealing with the reflection of light by spherical mirrors, we shall

follow a set of sign conventions called the New Cartesian Sign

Convention. In this convention, the pole (P) of the mirror is taken as the

origin (Fig. 9.9). The principal axis of the mirror is taken as the x-axis

(X’X) of the coordinate system. The conventions are as follows –

(i) The object is always placed to the left of the mirror. This implies

that the light from the object falls on the mirror from the left-hand

side.

(ii) All distances parallel to the principal axis are measured from the

pole of the mirror.

(iii) All the distances measured to the right of the origin (along

+ x-axis) are taken as positive while those measured to the left of

the origin (along – x-axis) are taken as negative.

(iv) Distances measured perpendicular to and above the principal axis

(along + y-axis) are taken as positive.

(v) Distances measured perpendicular to and below the principal axis

(along –y-axis) are taken as negative.

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The New Cartesian Sign Convention described above is illustrated in

Fig.9.9 for your reference. These sign conventions are applied to obtain

the mirror formula and solve related numerical problems.

9.2.4 Mirror Formula and Magnification

In a spherical mirror, the distance of the

object from its pole is called the object

distance (u). The distance of the image from

the pole of the mirror is called the image

distance (v). You already know that the

distance of the principal focus from the pole

is called the focal length (f). There is a

relationship between these three quantities

given by the mirror formula which is

expressed as

1 1 1

v u f

+ =

(9.1)

This formula is valid in all situations for all

spherical mirrors for all positions of the

object. You must use the New Cartesian Sign

Convention while substituting numerical

values for u, v, f, and R in the mirror formula

for solving problems.

Magnification

Magnification produced by a spherical mirror gives the relative extent to

which the image of an object is magnified with respect to the object size.

It is expressed as the ratio of the height of the image to the height of the

object. It is usually represented by the letter m.

If h is the height of the object and h

′

is the height of the image, then

the magnification m produced by a spherical mirror is given by

m =

Height of the image ( )

Height of the object ( )

′h

m =

′h

(9.2)

The magnification m is also related to the object distance (u) and

image distance (v). It can be expressed as:

Magnification (m) =

′

= −

(9.3)

You may note that the height of the object is taken to be positive as

the object is usually placed above the principal axis. The height of the

image should be taken as positive for virtual images. However, it is to be

taken as negative for real images. A negative sign in the value of the

magnification indicates that the image is real. A positive sign in the value

of the magnification indicates that the image is virtual.

Figure 9.9Figure 9.9

Figure 9.9

The New Cartesian Sign Convention for spherical mirrors

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The SI unit of power of a lens is ‘dioptre’. It is denoted by the letter D.

If f is expressed in metres, then, power is expressed in dioptres. Thus,

1 dioptre is the power of a lens whose focal length is 1 metre. 1D = 1m

–1

You may note that the power of a convex lens is positive and that of a

concave lens is negative.

Opticians prescribe corrective lenses indicating their powers. Let us

say the lens prescribed has power equal to + 2.0 D. This means the lens

prescribed is convex. The focal length of the lens is + 0.50 m. Similarly,

a lens of power – 2.5 D has a focal length of – 0.40 m. The lens is concave.

Many optical instruments consist of a number of lenses. They are combined to increase

the magnification and sharpness of the image. The net power (P) of the lenses placed

in contact is given by the algebraic sum of the individual powers P

, P

, … as

P = P

+ P

+ …

The use of powers, instead of focal lengths, for lenses is quite convenient for opticians.

During eye-testing, an optician puts several different combinations of corrective lenses

of known power, in contact, inside the testing spectacles’ frame. The optician calculates

the power of the lens required by simple algebraic addition. For example, a combination

of two lenses of power + 2.0 D and + 0.25 D is equivalent to a single lens of power + 2.25 D.

The simple additive property of the powers of lenses can be used to design lens systems

to minimise certain defects in images produced by a single lens. Such a lens system,

consisting of several lenses, in contact, is commonly used in the design of lenses of

camera, microscopes and telescopes.

QUESTIONS

1. Define 1 dioptre of power of a lens.

2. A convex lens forms a real and inverted image of a needle at a distance

of 50 cm from it. Where is the needle placed in front of the convex lens

if the image is equal to the size of the object? Also, find the power of the

lens.

3. Find the power of a concave lens of focal length 2 m.

What you have learnt

n Light seems to travel in straight lines.

n Mirrors and lenses form images of objects. Images can be either real or virtual,

depending on the position of the object.

n The reflecting surfaces, of all types, obey the laws of reflection. The refracting

surfaces obey the laws of refraction.

n New Cartesian Sign Conventions are followed for spherical mirrors and lenses.

More to Know!

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n Mirror formula,

1 1 1

+ =

v u f

, gives the relationship between the object-distance (u),

image-distance (v), and focal length (f) of a spherical mirror.

n The focal length of a spherical mirror is equal to half its radius of curvature.

n The magnification produced by a spherical mirror is the ratio of the height of the

image to the height of the object.

n A light ray travelling obliquely from a denser medium to a rarer medium bends

away from the normal. A light ray bends towards the normal when it travels obliquely

from a rarer to a denser medium.

n Light travels in vacuum with an enormous speed of 3×10

m s

-1

. The speed of light

is different in different media.

n The refractive index of a transparent medium is the ratio of the speed of light in

vacuum to that in the medium.

n In case of a rectangular glass slab, the refraction takes place at both air-glass

interface and glass-air interface. The emergent ray is parallel to the direction of

incident ray.

n Lens formula,

1 1 1

– =

v u f

, gives the relationship between the object-distance (u),

image-distance (v), and the focal length (f) of a spherical lens.

n Power of a lens is the reciprocal of its focal length. The SI unit of power of a lens is

dioptre.

EXERCISES

1. Which one of the following materials cannot be used to make a lens?

(a) Water (b) Glass (c) Plastic (d) Clay

2. The image formed by a concave mirror is observed to be virtual, erect and larger

than the object. Where should be the position of the object?

(a) Between the principal focus and the centre of curvature

(b) At the centre of curvature

(d) Between the pole of the mirror and its principal focus.

3. Where should an object be placed in front of a convex lens to get a real image of the

size of the object?

(a) At the principal focus of the lens

(b) At twice the focal length

(d) Between the optical centre of the lens and its principal focus.

4. A spherical mirror and a thin spherical lens have each a focal length of –15 cm. The

mirror and the lens are likely to be

(a) both concave.

(b) both convex.

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